(57) An apparatus and method are provided in order to handle a plurality of stacks (28), such as stacks of sliced food products including luncheon meats. Product stacks are stopped during their flow along a conveyor (21) pathway, the stoppage being at a location for generally vertical alignment with an overhead picker head (26). The picker head grasps the thus positioned stacks and moves same to a location above and in general vertical alignment with a cavity of a packaging container for the stacks of sliced product, at which time the stacks are released, and the product stacks enter the cavities which are subsequently closed to provide finished packaged products.